气体辅助注射成型充模机理数值模拟与成型工艺稳健优化
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摘要
气体辅助注射成型(简称气辅成型)是一种新型的聚合物成型工艺。该工艺先将聚合物熔体部分或全部注入模腔,紧接着把压缩空气注入到聚合物熔体内部来推动塑料熔体充满整个模腔,形成中空气道。与传统注塑成型工艺相比,气辅成型可以提高产品表面质量、减少翘曲变形、降低锁模力、减轻制品重量、节省费用。但另一方面,气辅成型工艺参数的增多导致其工艺更加难于控制,实际生产中工艺参数的波动、噪声因素的存在也会导致气辅成型废品率的上升。
随着计算机技术与有限元理论快速发展,气辅成型数值模拟也得到了快速发展。基于数值模拟的气辅成型优化可以减少繁琐的试模与人工修改,帮助设计人员快速、有效地寻找到最优参数组合。但气辅成型CAE和工艺优化研究还存在以下一些问题:
首先,基于Hele-Shaw假设的数值模拟方法将作用于熔体的气体简化为压力边界条件,不能精确描述气体、熔体两相的相互作用机理。其次,气辅成型工艺参数与设计响应之间具有非线性隐式关系,传统基于梯度的优化算法面对这样问题显得无能为力。传统的优化算法还要同时面对复杂零件CAE分析的计算成本问题。最后,气辅成型产品的质量指标评判存在多种准则,不同质量指标之间通常相互冲突,难于通过加权方式调和,因此有必要协调多目标之间的关系并降低优化目标受设计波动的影响程度。
针对气辅成型工艺在实际应用中迫切需要解决的问题,本文着重从以下几个方面对其进行研究:
首先提出将模腔内的气体、熔体用统一的N-S方程描述,将作用于熔体上的气体也当作流体来处理,赋予其运动控制方程、恒定的粘度和密度,采用VOF方法跟踪气熔两相边界。将气辅成型气体穿透模拟简化为两相流体瞬态流动速度场、压力场求解的流体动力学问题。
基于本文提出的气辅穿透机理计算模型,针对常见气辅成型零件特征,提出几种典型形状气道几何模型,并对其穿透进行数值模拟。相对于基于Hele-Shaw假设的模拟,该模型可以准确、有效地模拟穿透过程中气∕熔两相边界,并获取气∕熔两相边界的变化规律,同时还捕捉到了气∕熔两相边界在通过气道拐角时候的运动规律。通过数值模拟结果解释了气道设计中的边角效应(Edge Shape)和拐角处圆角效应,并给出了合理设计气道参数的建议。
其次,本文提出了基于CAE模拟、代理模型和智能进化算法的集成优化策略,对粒子群智能进化算法(PSO)进行了合理改进,开发了基于Matlab平台的自适应PSO算法。该算法以CAE分析为实验手段,采用拉丁超立方取样方法,使样本点均匀分布于解空间,采用合适的多项式和高斯函数作为相关函数,建立起映射工艺参数与优化目标之间非线性关系的Kriging近似模型,并由自适应PSO算法在解空间搜寻最优解。自适应PSO算法可以加快优化算法的收敛速度,以较小的计算成本获取最佳参数组合。
本文还重点讨论了多目标问题处理方法,提出了基于CAE和代理模型的多目标优化策略。将基于拥挤距离的机制和变异算子引入PSO算法,基于Matlab平台实现Multi-Objective Particle Swarm Optimization Based On Crowding Distance (MOPSOCD)算法。拥挤距离机制和变异算子可以保持计算所得非支配解具有较好的空间分布特性,保持粒子群种群的多样性。在多目标粒子群算法中引入外部种群,用以保存进化过程中不断产生的非支配解,可以最大限度的发掘可行解空间中存在的非支配解,保证了进化算法的全局搜索能力。将其与基于CAE和代理模型的优化设计程序集成,显著提高了优化效率,改善了Pareto解分布。
针对实际工程优化中忽略不确定因素的影响,时常导致设计失效的问题,本文将稳健设计方法应用到气体辅助注射成型优化。通过引入可靠性设计和6-sigma质量管理思想,将设计质量提高到6-sigma水平。对稳健优化准则进行了详细分析,提出了稳健优化的多目标处理原则,将稳健优化当做多目标问题进行求解。针对CAE模拟的计算量问题,将代理模型技术与蒙特卡洛方法结合,构造出基于代理模型和蒙特卡洛模拟的稳健优化策略。
最后,将6-sigma稳健优化设计方法应用到复杂且产品厚度分布不均匀的汽车后视镜气辅成型优化设计,获得了一系列Pareto稳健设计解。该方法相对于确定性优化设计,其可靠性和稳健性有了显著提高。相对于加权方法处理稳健问题,本方法得到的一系列稳健设计解可以为气辅成型工艺设计提供更多的可选方案。
Gas Assisted Injection Molding (GAIM) is one of the most important and innovative molding process. In GAIM, the polymer melt is firstly filled or partially filled into mold cavity, and then the compressed gas is injected into the mold to drive the molten polymer further into the mold, leaving a hollow gas channel in the part. The GAIM can not only reduce warpage, clamping force and product weight, but also improve surface quality and save costs compared with the traditional injection molding. On the other hand, there are many unstable factors which can effects product quality of GAIM in actual production, it will result in the control of GAIM become harder compared with injection molding, because new parameters are introduced to GAIM. Fluctuation of design and parameters and the noise factor will lead to the increase of waste product rate too.
With the development of computer technology and Finite Element Method (FEM) theory, rapid progress has been made in the numerical simulation of GAIM. The processing optimization of GAIM based on numerical simulation can reduce the numbers of“trial and error”, and help designers obtain best process parameters quickly and effectively. There are several issues in numerical simulation and processing optimization of GAIM:
Firstly, the simulation based on Hele-Shaw hypothesis treats the gas imposed on polymer melt as the boundary conditions simply. It can’t describe the flow mechanism of gas and melt. Secondly, the relationship between process parameters and design response is recessive and nonlinear, traditional optimization algorithm based on gradient is not suitable for this kind of problem, and traditional optimization algorithm is time consuming and costly especially for the complex parts. Last, there are several kinds of criteria for the quality of GAIM parts,different kinds of criteria is conflict usually, it can’t be solved by weighted methods simply. Therefore, it is necessary to coordinate the relationship between different goals and reduce the sensitivity of processing fluctuations.
These are some key technical problems which should be solved in GAIM now. The main topics of the thesis are as follows:
Firstly, the melt and gas in mold should be described by unified N-S equations, the gas which is act on polymer melt is treated as fluid too, therefore the gas should be endow with governing equations, constant density and viscosity. The VOF method is obtained to trace the free-interface of gas and polymer melt. Finally, the gas penetration of GAIM is simplified to the computation of velocity and pressure fields of two phase flow.
Based on the governing equations and common shape of GAIM parts, different typical gas channel were modeled and simulated. Compared with the Hele-Shaw hypothesis, the free-interface of gas and polymer melt can be simulated exactly, the variation of free-interface can be obtained, and the motion pattern of free-interface can also be captured when the gas pass through the corner of gas channel. The edge shape of gas channel and the fillet effect are interpreted by simulation, and the recommended values of gas channel are proposed too.
Secondly, a hybrid optimization approach, which is integrates CAE, surrogate model and intelligent evolution algorithm, is proposed. The Adaptive particle swarm optimization (APSO) algorithm is developed by Matlab. In this approach, the CAE is adopted as experimental means, the Latin Hypercube Sampling method (LHS), which can fill the whole design space, is used to sampling in feasible design space, the Kriging surrogate model is adopted to approximate the nonlinear relationship between processing parameters and optimization objective, APSO algorithm is adopted to search optimal solutions. APSO can accelerate the convergence rate of optimization approach, and obtain optimal processing parameters using the least computational costs.
The Multi-Objective optimization method is discussed. The Multi-Objective optimization approach which is based on surrogate model, CAE is proposed. The Multi-Objective PSO Based on Crowding Distance (MOPSOCD) is developed based on Matlab platform by introducing Crowding distance mechanism and mutation operator. The crowing distance mechanism and mutation operator can maintain the diversity of population.
The external archive can constantly save the non-dominate solutions generated by algorithm, it can search the non-dominate solutions as many as possible and guarantee the global optimization. Integrating it with the optimization approach based on CAE and surrogate model, both the efficiency of approach and distribution of Pareto solutions are improved.
According to the design failure caused by uncertain factors in real GAIM processing, the robust design is introduced to the optimization of GAIM. By introducing reliability design and 6-sigma quality theory, the design quality can be improved to 6-sigma level. The robust design criterion is analyzed. Robust design is generally focused on reducing response variation, balancing“mean on target”and“minimize variation”performance objectives. So, the 6-sigma robust design is treated as multi-objective problem in this thesis. The computation costs caused by CAE are solved by integrating Monte Carlo Simulation with surrogate model.
Finally, by applying 6-sigma robust design to a car back mirror which is molding by GAIM, a series of Pareto robust solutions are obtained. Compared with the deterministic optimization, the reliability and robustness are improved significantly. The robust solutions obtained by this approach can provide more optional scheme for the processing design of GAIM.
随着计算机技术与有限元理论快速发展,气辅成型数值模拟也得到了快速发展。基于数值模拟的气辅成型优化可以减少繁琐的试模与人工修改,帮助设计人员快速、有效地寻找到最优参数组合。但气辅成型CAE和工艺优化研究还存在以下一些问题:
首先,基于Hele-Shaw假设的数值模拟方法将作用于熔体的气体简化为压力边界条件,不能精确描述气体、熔体两相的相互作用机理。其次,气辅成型工艺参数与设计响应之间具有非线性隐式关系,传统基于梯度的优化算法面对这样问题显得无能为力。传统的优化算法还要同时面对复杂零件CAE分析的计算成本问题。最后,气辅成型产品的质量指标评判存在多种准则,不同质量指标之间通常相互冲突,难于通过加权方式调和,因此有必要协调多目标之间的关系并降低优化目标受设计波动的影响程度。
针对气辅成型工艺在实际应用中迫切需要解决的问题,本文着重从以下几个方面对其进行研究:
首先提出将模腔内的气体、熔体用统一的N-S方程描述,将作用于熔体上的气体也当作流体来处理,赋予其运动控制方程、恒定的粘度和密度,采用VOF方法跟踪气熔两相边界。将气辅成型气体穿透模拟简化为两相流体瞬态流动速度场、压力场求解的流体动力学问题。
基于本文提出的气辅穿透机理计算模型,针对常见气辅成型零件特征,提出几种典型形状气道几何模型,并对其穿透进行数值模拟。相对于基于Hele-Shaw假设的模拟,该模型可以准确、有效地模拟穿透过程中气∕熔两相边界,并获取气∕熔两相边界的变化规律,同时还捕捉到了气∕熔两相边界在通过气道拐角时候的运动规律。通过数值模拟结果解释了气道设计中的边角效应(Edge Shape)和拐角处圆角效应,并给出了合理设计气道参数的建议。
其次,本文提出了基于CAE模拟、代理模型和智能进化算法的集成优化策略,对粒子群智能进化算法(PSO)进行了合理改进,开发了基于Matlab平台的自适应PSO算法。该算法以CAE分析为实验手段,采用拉丁超立方取样方法,使样本点均匀分布于解空间,采用合适的多项式和高斯函数作为相关函数,建立起映射工艺参数与优化目标之间非线性关系的Kriging近似模型,并由自适应PSO算法在解空间搜寻最优解。自适应PSO算法可以加快优化算法的收敛速度,以较小的计算成本获取最佳参数组合。
本文还重点讨论了多目标问题处理方法,提出了基于CAE和代理模型的多目标优化策略。将基于拥挤距离的机制和变异算子引入PSO算法,基于Matlab平台实现Multi-Objective Particle Swarm Optimization Based On Crowding Distance (MOPSOCD)算法。拥挤距离机制和变异算子可以保持计算所得非支配解具有较好的空间分布特性,保持粒子群种群的多样性。在多目标粒子群算法中引入外部种群,用以保存进化过程中不断产生的非支配解,可以最大限度的发掘可行解空间中存在的非支配解,保证了进化算法的全局搜索能力。将其与基于CAE和代理模型的优化设计程序集成,显著提高了优化效率,改善了Pareto解分布。
针对实际工程优化中忽略不确定因素的影响,时常导致设计失效的问题,本文将稳健设计方法应用到气体辅助注射成型优化。通过引入可靠性设计和6-sigma质量管理思想,将设计质量提高到6-sigma水平。对稳健优化准则进行了详细分析,提出了稳健优化的多目标处理原则,将稳健优化当做多目标问题进行求解。针对CAE模拟的计算量问题,将代理模型技术与蒙特卡洛方法结合,构造出基于代理模型和蒙特卡洛模拟的稳健优化策略。
最后,将6-sigma稳健优化设计方法应用到复杂且产品厚度分布不均匀的汽车后视镜气辅成型优化设计,获得了一系列Pareto稳健设计解。该方法相对于确定性优化设计,其可靠性和稳健性有了显著提高。相对于加权方法处理稳健问题,本方法得到的一系列稳健设计解可以为气辅成型工艺设计提供更多的可选方案。
Gas Assisted Injection Molding (GAIM) is one of the most important and innovative molding process. In GAIM, the polymer melt is firstly filled or partially filled into mold cavity, and then the compressed gas is injected into the mold to drive the molten polymer further into the mold, leaving a hollow gas channel in the part. The GAIM can not only reduce warpage, clamping force and product weight, but also improve surface quality and save costs compared with the traditional injection molding. On the other hand, there are many unstable factors which can effects product quality of GAIM in actual production, it will result in the control of GAIM become harder compared with injection molding, because new parameters are introduced to GAIM. Fluctuation of design and parameters and the noise factor will lead to the increase of waste product rate too.
With the development of computer technology and Finite Element Method (FEM) theory, rapid progress has been made in the numerical simulation of GAIM. The processing optimization of GAIM based on numerical simulation can reduce the numbers of“trial and error”, and help designers obtain best process parameters quickly and effectively. There are several issues in numerical simulation and processing optimization of GAIM:
Firstly, the simulation based on Hele-Shaw hypothesis treats the gas imposed on polymer melt as the boundary conditions simply. It can’t describe the flow mechanism of gas and melt. Secondly, the relationship between process parameters and design response is recessive and nonlinear, traditional optimization algorithm based on gradient is not suitable for this kind of problem, and traditional optimization algorithm is time consuming and costly especially for the complex parts. Last, there are several kinds of criteria for the quality of GAIM parts,different kinds of criteria is conflict usually, it can’t be solved by weighted methods simply. Therefore, it is necessary to coordinate the relationship between different goals and reduce the sensitivity of processing fluctuations.
These are some key technical problems which should be solved in GAIM now. The main topics of the thesis are as follows:
Firstly, the melt and gas in mold should be described by unified N-S equations, the gas which is act on polymer melt is treated as fluid too, therefore the gas should be endow with governing equations, constant density and viscosity. The VOF method is obtained to trace the free-interface of gas and polymer melt. Finally, the gas penetration of GAIM is simplified to the computation of velocity and pressure fields of two phase flow.
Based on the governing equations and common shape of GAIM parts, different typical gas channel were modeled and simulated. Compared with the Hele-Shaw hypothesis, the free-interface of gas and polymer melt can be simulated exactly, the variation of free-interface can be obtained, and the motion pattern of free-interface can also be captured when the gas pass through the corner of gas channel. The edge shape of gas channel and the fillet effect are interpreted by simulation, and the recommended values of gas channel are proposed too.
Secondly, a hybrid optimization approach, which is integrates CAE, surrogate model and intelligent evolution algorithm, is proposed. The Adaptive particle swarm optimization (APSO) algorithm is developed by Matlab. In this approach, the CAE is adopted as experimental means, the Latin Hypercube Sampling method (LHS), which can fill the whole design space, is used to sampling in feasible design space, the Kriging surrogate model is adopted to approximate the nonlinear relationship between processing parameters and optimization objective, APSO algorithm is adopted to search optimal solutions. APSO can accelerate the convergence rate of optimization approach, and obtain optimal processing parameters using the least computational costs.
The Multi-Objective optimization method is discussed. The Multi-Objective optimization approach which is based on surrogate model, CAE is proposed. The Multi-Objective PSO Based on Crowding Distance (MOPSOCD) is developed based on Matlab platform by introducing Crowding distance mechanism and mutation operator. The crowing distance mechanism and mutation operator can maintain the diversity of population.
The external archive can constantly save the non-dominate solutions generated by algorithm, it can search the non-dominate solutions as many as possible and guarantee the global optimization. Integrating it with the optimization approach based on CAE and surrogate model, both the efficiency of approach and distribution of Pareto solutions are improved.
According to the design failure caused by uncertain factors in real GAIM processing, the robust design is introduced to the optimization of GAIM. By introducing reliability design and 6-sigma quality theory, the design quality can be improved to 6-sigma level. The robust design criterion is analyzed. Robust design is generally focused on reducing response variation, balancing“mean on target”and“minimize variation”performance objectives. So, the 6-sigma robust design is treated as multi-objective problem in this thesis. The computation costs caused by CAE are solved by integrating Monte Carlo Simulation with surrogate model.
Finally, by applying 6-sigma robust design to a car back mirror which is molding by GAIM, a series of Pareto robust solutions are obtained. Compared with the deterministic optimization, the reliability and robustness are improved significantly. The robust solutions obtained by this approach can provide more optional scheme for the processing design of GAIM.
引文
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